On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion
On arbitrage‐free pricing of weather derivatives based on fractional Brownian motion
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DOI：
10.1080/1350486032000174628
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发表时间：
2003-12
影响因子：
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通讯作者：
F. Benth
中科院分区：
文献类型：
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作者：
F. Benth
我们得到了温度索赔的无套利定价动力学，其中温度服从分数Ornstein-Uhlenbeck过程。利用分数阶白噪声演算，可以将动力学表示为一种特殊类型的条件期望，而不是经典的条件期望。利用傅立叶变换技术，导出了欧式索赔和平均型索赔的显式表达式，并证明了这些定价公式是某些Black和Scholes偏微分方程解。我们的结果部分证实了Brody、Syroka和Zervos的猜想。
We derive an arbitrage‐free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein–Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos.